By making use of the preconditioned Hermitian and skew-Hermitian splitting (PHSS) iteration as the inner solver for the modified Newton method, we establish the modified Newton-PHSS method for solving large sparse systems of nonlinear equations with positive definite Jacobian matrices at the solution points. Moreover, the local convergence theorem is proved under proper conditions. Numerical results are given to show its feasibility and effectiveness. In addition, the advantages of the modified Newton-PHSS method over some other methods are shown by solving two systems of nonlinear equations.

中文翻译：

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修正的Newton-PHSS方法求解带正定Jacobian矩阵的非线性系统

通过使用预处理的Hermitian和skew-Hermitian分裂（PHSS）迭代作为改进的Newton方法的内部求解器，我们建立了改进的Newton-PHSS方法，用于求解带有正定Jacobian矩阵的非线性方程的大型稀疏系统点。此外，在适当条件下证明了局部收敛定理。数值结果表明了该方法的可行性和有效性。此外，通过求解两个非线性方程组，显示了改进的Newton-PHSS方法相对于其他方法的优势。